[Farsight]

General relativity is all about measurements of time and distance, geezer. It's quite simple really, but it usually isn't explained very well. People tend to start with "curved spacetime", and they don't tell you why it's curved. IMHO it's better to think about it as curvilinear motion caused by inhomogeneous space caused in turn by the concentration of energy tied up as the matter of a planet. This is what Einstein said about general relativity in 1920:

"According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that “empty space” in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials g_μν)..."
 
Space in a gravitational field isn't homogeneous. It has a lower g_μν below you, and a higher g_μν above. Between them there's a gradient. It's like an "energy density gradient". So when you move through it like a photon, you veer, downwards. Since we measure space and time using the motion of light, we say space-time is curved, and that you follow a null geodesic. You tend not to find this kind of description when you look it up and the internet, but it is in line with what Einstein said. It's accepted physics. What he didn't actually say and what isn't accepted physics is this: if you're just sitting there in space like an electron, the electron has spin, so internally it's moving in little circles. Hence part of your path is subject to veer, so you work yourself down - the brick falls down because it's composed of electrons and things with spin. I don't know why this isn't accepted physics, but I think it will be in time.

[PhysBang]

You tend not to find this kind of description when you look it up and the internet, but it is in line with what Einstein said. It's accepted physics. What he didn't actually say and what isn't accepted physics is this: if you're just sitting there in space like an electron, the electron has spin, so internally it's moving in little circles. Hence part of your path is subject to veer, so you work yourself down - the brick falls down because it's composed of electrons and things with spin. I don't know why this isn't accepted physics, but I think it will be in time.

It's quite obvious why this isn't accepted physics: it cannot be used to actually produce predictions of the motions of electrons.

[Farsight]

PhysBang: some imagined mathematical deficiency is no substitute for the experimental fact that pair production creates an electron and a positron from light, that electrons and positrons exhibit the properties of angular momentum and magnetic moment and can be diffracted like light, and that the product of electron/positron annihilation is light. See The Nature of the Electron by Qiu-Hong Hu (Physics Essays, Vol. 17, No. 4, 2004) at http://arxiv.org/abs/physics/0512265 along with Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime by Ye Xing-Hao et al (Chinese Phys. Lett. 25 1571-1574 2008) at http://www.iop.org/EJ/abstract/0256-307X/25/5/014. You may also wish to peruse The Refractive Index in Electron Optics and the Principles of Dynamics by Ehrenberg and Siday (Proc. Phys. Soc. B62: 8–21 1949). I'm sorry, but these are bona-fide peer-reviewed papers, dismissal and denial is no longer an option.

Now please, can we stay on topic. If you wish to assist on this thread, give geezer the initial understanding of general relativity which he seeks.

[JP]

PhysBang: some imagined mathematical deficiency is no substitute for the experimental fact that pair production creates an electron and a positron from light, that electrons and positrons exhibit the properties of angular momentum and magnetic moment and can be diffracted like light, and that the product of electron/positron annihilation is light. See The Nature of the Electron by Qiu-Hong Hu (Physics Essays, Vol. 17, No. 4, 2004) at http://arxiv.org/abs/physics/0512265 along with Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime by Ye Xing-Hao et al (Chinese Phys. Lett. 25 1571-1574 2008) at http://www.iop.org/EJ/abstract/0256-307X/25/5/014. You may also wish to peruse The Refractive Index in Electron Optics and the Principles of Dynamics by Ehrenberg and Siday (Proc. Phys. Soc. B62: 8–21 1949). I'm sorry, but these are bona-fide peer-reviewed papers, dismissal and denial is no longer an option.

It's a big jump from being able to treat curvature of space-time as an index of refraction for light (or electron) beams to saying that electrons have a helical structure.  The first article that makes claims about the electron having some odd helical structure is published in Physics Essays, which, while peer-reviewed, accepts a lot of papers on fringe topics that don't have mainstream acceptance. 

Now please, can we stay on topic. If you wish to assist on this thread, give geezer the initial understanding of general relativity which he seeks.

I do have a question relating to the thread topic:

The concept of work in classical mechanics is useful in dealing with conservation of energy, since it tells you how you can add or subtract energy from a system, especially a system in a potential.  So my question is this: does conservation of energy hold in GR?  And if it does or doesn't, could someone explain why or why not?  (Just from the fact that gravity isn't treated as a force and that it deals with non-inertial reference frames, I would think you'd run into problems...)

[Farsight]

It's a big jump from being able to treat curvature of space-time as an index of refraction for light (or electron) beams to saying that electrons have a helical structure. The first article that makes claims about the electron having some odd helical structure is published in Physics Essays, which, while peer-reviewed, accepts a lot of papers on fringe topics that don't have mainstream acceptance.

The issue of mainstream acceptance and the exact structure can be debated, JP, but the "made of light" and the rotational evidence remains. Another paper on this theme is "Is the electron a photon with a toroidal topology?" by Williamson and van der Mark (Annales de la Fondation Louis de Broglie, Volume 22, no.2, 133 1997). These are former CERN scientists, and it took them six years to get this into a journal. You can download a version from http://www.cybsoc.org/cybcon2008prog.htm#jw.   

..The concept of work in classical mechanics is useful in dealing with conservation of energy, since it tells you how you can add or subtract energy from a system, especially a system in a potential.  So my question is this: does conservation of energy hold in GR?...

Yes. See the link above to http://www.ddart.net/science/physics/physics_tutorial/Class/energy/U5L2a.html which says:

"When work is done upon an object by an internal force (for example, gravitational and spring forces), the total mechanical energy (KE + PE) of that object remains constant. In such cases, the object's energy changes form. For example, as an object is "forced" from a high elevation to a lower elevation by gravity, some of the potential energy of that object is transformed into kinetic energy. Yet, the sum of the kinetic and potential energies remain constant. This is referred to as energy conservation and will be discussed in detail later in this lesson. When the only forces doing work are internal forces, energy changes forms - from kinetic to potential (or vice versa); yet the total amount of mechanical [energy] is conserved."

When a brick falls down, some of the potential energy associated with internalised motion becomes the kinetic energy of macroscopic motion. The reduced rate of internalised motion is accounted for by gravitational time dilation, and gravity is adding no energy to the brick.

All: I'm tied up for the next few days, and will be offline.

[JP]

Farsight, Annales de la Fondation Louis de Broglie is another fringe journal that publishes a lot of non-mainstream physics.  I wouldn't rely on that for citations that a theory is valid.  At any rate, the helical-electron theory is certainly not mainstream and therefore doesn't really answer the question about work in a gravitational field--at least not in terms of accepted physical theories.

[litespeed]

lightarrow - You wrote: "About the second question, Farsight explained it: when you lift a payload with a rocket, the rocket engine *does* make work on the payload, increasing its energy and so its mass, from M to M + ΔM; when the payload falls, the ΔM becomes kinetic energy."

This is were I become confused. We know that GPS satellites need to be corrected for two separate effects. First, removing them further from the center of gravity speeds up their time by a given amount. In addition, accelerating them slows down their time, but by a lesser amount. Accordingly GPS satellite clocks actually run faster then those on the ground.

So here is my question. Have the satellites gained or lost mass?

[lightarrow]

lightarrow - You wrote: "About the second question, Farsight explained it: when you lift a payload with a rocket, the rocket engine *does* make work on the payload, increasing its energy and so its mass, from M to M + ΔM; when the payload falls, the ΔM becomes kinetic energy."

This is were I become confused. We know that GPS satellites need to be corrected for two separate effects. First, removing them further from the center of gravity speeds up their time by a given amount. In addition, accelerating them slows down their time, but by a lesser amount. Accordingly GPS satellite clocks actually run faster then those on the ground.

So here is my question. Have the satellites gained or lost mass?

With respect to when they are still on the Earth surface, they should have gained mass. Anyway, the subject is quite complicated for me, I'm not sure I'll be able to give many more details.

[yor_on]

This is how I see it, SpaceTime's gravity is a geometry we cant see. Take gravitational waves f.ex . No matter their 'velocity' they will still be distortions of SpaceTime and when they pass through us we will deform slightly. Gravity also creates what we call 'gravity wells' where matter rests at its 'bottom'. So to do work you will have to oppose gravity, going out from that well.

The whole discussion of 'potential energy' circles around the effect we can observe when a object in 'free fall' gets stopped by matter on its journey. what we call its acceleration is its balance relative that well, depending on the gravity-wells mass.

All objects move, if uniformly or 'accelerating' doesn't matter, you can always think up another object existing in relative 'non motion' relative it. All of those things are definitions relative something else. 'Work' as an abstract idea is when you do something that's contrary to the 'easiest path'. The more you go of the path of non resistance, the more work you will have to do. It's a general rule, fitting almost anything I can think of

Like if photons really, from our perspective, never would bend towards mass, and instead alway keep a straight line. If that would happen in our SpaceTime then that light would 'do work.' That it doesn't do so does not mean that it bends, even though it seems so from our perspective. Light will always take the straight path through SpaceTime as shaped by gravity, it's just us unable to see those dips and bends.

You can f. ex. have an situation where you see it as you are 'doing work' on a object that as seen from another frame just is in a 'free fall'.

To me work will be that what opposes, generally speaking

[Geezer]

Farsight - Here's the reference you quoted in your most recent post.

"When work is done upon an object by an internal force (for example, gravitational and spring forces), the total mechanical energy (KE + PE) of that object remains constant. In such cases, the object's energy changes form. For example, as an object is "forced" from a high elevation to a lower elevation by gravity, some of the potential energy of that object is transformed into kinetic energy. Yet, the sum of the kinetic and potential energies remain constant."

It is critical that we understand the meaning of the last sentence. While the brick is changing position relative to the Earth, the last sentence would seem to apply. However, when the body stops changing position relative to the Earth, the last sentence no longer holds.

When the brick comes to rest on the Earth, it has zero kinetic energy, and it has reduced potential energy.

Furthermore, the brick has the same mass that it had when we let it drop. What happened to the mass between the two states may be interesting, but it's unimportant.

At the end of the experiment, the brick has reduced energy. I'm reasonably confident that no energy was annihilated or converted into matter during this experiment, so it's likely that the total energy in the system is conserved, but it sure ain't conserved in the brick!

Energy was expended (or, more accurately, transferred to some other part of the system) in moving the brick. Therefore, work was done.

Don't get me wrong. I would like to repeal the Third Law of Thermodynamics as much as anyone, it's just that I don't think this experiment demonstrates a loophole in that law.

I think it's always important to remember that, whereas the large print giveth plenty, the small print taketh away more. Or, if you prefer, the only way to prevent entropy from winning is to do nothing.

[JP]

So I think that the idea of work isn't the fundamental concept.  The fundamental concept is conservation of energy, since work tells you that you're basically transferring energy from kinetic to potential (or into other forms of energy) via "work."  Therefore, it's probably easiest to start with conservation of energy.

I did a bit of reading up on the conservation of energy in general relativity.  I can follow much of the math, but I only partly follow the physical implications of it. 

Basically everyone seems to agree that GR in general does not satisfy conservation of energy if you include all the non-gravitational energy.  If the geometry of space-time gets "flat" (i.e. gravity dies away) as you move infinitely far away, then the non-gravitational energy is conserved over that large volume.  The problem with GR and conservation of energy is that the equations of GR take as their "energy" term what is called the stress-energy tensor, which measures only non-gravitational energy, and says that the curvature of space is caused by this non-gravitational energy.  In order to conserve energy over a small region of space, you also need to include gravitational energy.  You can do this by tacking a a new term onto your stress-energy tensor to include gravity.

I think the analogue of this in Newtonian gravity would be that the energy of the brick itself isn't conserved while it's falling, but the energy of the brick plus its gravitational potential is.  Unlike the Newtonian case, the equations for gravity don't include a gravitational energy (or force) term, but instead specify it according to geometry, so I guess that's why you would need to go back after the fact and say that the term you're adding (to get conservation of energy) is due to gravity.  Finally, a problem with this formulation is that although energy conservation derived from this pseudotensor holds in all reference frames, the stress energy pseudotensor (the one with the gravitational energy added) isn't necessarily invariant in different reference frames, while the usual stress-energy tensor is.  I think this means that the term you're calling gravitational energy changes depending on your reference frame. 

What does this mean for work?  I think you would be in trouble trying to define it, since it would involve energy transfer between the gravitational field and "everything else."  You could define the "everything else" part just fine, but defining the gravitational field part would probably be problematic because it would depend on your reference frame. 

I'm not sure if this all makes sense, as I'm still trying to digest what I've read down to a simple form that makes sense...

Edit: I think a problem with considering classical examples as evidence of why work has to be defined in general relativity is that classical examples necessarily mean that the gravitational effects are weak.  To notice problems with the formulation of work, you would have to have a very strong gravitational field that ends up warping space and time in a way such that classical intuition wouldn't hold--or at least so that you couldn't observe the brick falling in the same way since the way you measure space and time doesn't match with the way the brick measures them.

[Farsight]

Farsight, Annales de la Fondation Louis de Broglie is another fringe journal that publishes a lot of non-mainstream physics. I wouldn't rely on that for citations that a theory is valid. At any rate, the helical-electron theory is certainly not mainstream and therefore doesn't really answer the question about work in a gravitational field - at least not in terms of accepted physical theories.

That was just another example, JP. Like I said, the detail is debateable. But pair production isn't, nor is electron angular momentum, nor gravitational time dilation. So the electron really is made of light, there's some kind of rotation or spin going on in there, and it occurs at a reduced rate down near the surface of a planet. It's all mainstream stuff.    

[Farsight]

Geezer: when the brick hits the ground, it kicks up debris etc. It does work doing all this, losing its kinetic energy. There will be heat too, which isn't actually classed as work, but it's the same kind of thing - it's essentially kinetic energy at the atomic scale, and the brick loses it. Yes, once the brick has come to rest on the earth, and cooled down, it has zero kinetic energy, and it has reduced potential energy. Yes, the total energy of the system is conserved, but some energy was transferred out of the brick when it hit the ground. Work was definitely done. Whether you say work was done when the brick hit the ground, or when the brick started falling, depends on the definition of work. Note though that whatever your choice here, and depite the brick appearing to have the same mass as it did when you dropped it, as per Einstein's 1905 paper, its final mass is slightly reduced because it has lost energy.

JP: take a look at the The Foundation of The General Theory of Relativity from about page 182 of document 30. Here it is http://www.alberteinstein.info/gallery/pdf/CP6Doc30_English_pp146-200.pdf, you'll be aware it's 3.6 Mbyte pdf. Einstein talks about conservation of energy and on says on page 185 "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". IMHO a simple form of this that makes sense, is to describe a region of space which exhibits a gravitational field as one that also exhibits a gradient in energy density. The energy density diminishes further away from the planet, so this isn't the the brick's potential energy, because the latter increases further away from the planet.

[lightarrow]

That was just another example, JP. Like I said, the detail is debateable. But pair production isn't, nor is electron angular momentum, nor gravitational time dilation. So the electron really is made of light, there's some kind of rotation or spin going on in there, and it occurs at a reduced rate down near the surface of a planet. It's all mainstream stuff.    

You are talking of not officially recognized theories here, certainly not "mainstream".

[Farsight]

I'm talking about scientific evidence, lightarrow. Search on:

Pair production

electron angular momentum

gravitational time dilation

We really do make an electron from light, it really does exhibit angular momentum aka spin, and gravitational time dilation is for real too. That's the evidence, regardless of the status of any theory.

[lightarrow]

I'm talking about scientific evidence, lightarrow. Search on:

Pair production

electron angular momentum

gravitational time dilation

We really do make an electron from light, it really does exhibit angular momentum aka spin, and gravitational time dilation is for real too. That's the evidence, regardless of the status of any theory.

There is something I'm missing. What:
-Pair production
-electron angular momentum
-gravitational time dilation
have to do with the fact the electron would be made of light?
When you say the electron is "made of light" I understand that its *inner structure* is light. Have I understood well?

[Geezer]

Geezer: when the brick hits the ground, it kicks up debris etc. It does work doing all this, losing its kinetic energy. There will be heat too, which isn't actually classed as work, but it's the same kind of thing - it's essentially kinetic energy at the atomic scale, and the brick loses it. Yes, once the brick has come to rest on the earth, and cooled down, it has zero kinetic energy, and it has reduced potential energy. Yes, the total energy of the system is conserved, but some energy was transferred out of the brick when it hit the ground. Work was definitely done. Whether you say work was done when the brick hit the ground, or when the brick started falling, depends on the definition of work. Note though that whatever your choice here, and depite the brick appearing to have the same mass as it did when you dropped it, as per Einstein's 1905 paper, its final mass is slightly reduced because it has lost energy.

OK - So the brick did work, but are you saying no work was done on the brick so that it was able to do work? And, if we raise the brick up again, can it recover the energy it lost unless we do work on it? Of course not.

Farsight - Your logic defies the Third Law of Thermodynamics. Even Einstein was not bold enough to attempt that.

[Farsight]

There is something I'm missing. What [does]:
-Pair production
-electron angular momentum
-gravitational time dilation
have to do with the fact the electron would be made of light? When you say the electron is "made of light" I understand that its *inner structure* is light. Have I understood well?

Maybe, lightarrow, but those three things together are to do with how gravity works on matter. Of those three things, only pair production is to do with the fact that the electron is made of light. We can't be sure of the structure, but what we can be sure of is that when we make an electron via pair production, we start with a nucleus and a gamma photon. We end up with a nucleus, and an electron, and a positron. The light has gone. Then when we annihilate an electron with a positron, what we get is gamma photons. That's the light back. Nothing else goes in, and nothing else comes out. So what's the electron made of? Light. Nothing else. There's not a lot to understand, the scientific evidence is there, it's cut and dried. But for some strange reason people don't seem to know about it.   

OK - So the brick did work, but are you saying no work was done on the brick so that it was able to do work? And, if we raise the brick up again, can it recover the energy it lost unless we do work on it? Of course not. Farsight - your logic defies the Third Law of Thermodynamics. Even Einstein was not bold enough to attempt that.

My logic is rock solid, Geezer. Like I said way back, when you lift the brick, you do work. You add energy to the brick. Drop the brick, and when it hits the ground, the brick does work. The energy you put into the brick by lifting it, goes into licking up a crater and heat etc. Whether work is being done by gravity as the brick is falling is debateable, and depends on your definition of work. If work is the transfer of energy from one form to another, gravity does work. But if work is the transfer of energy into or out of the brick, it doesn't. LOL, it's a bit like this:

Q: Will a fall kill you?
A: No. But the sudden stop at the end of the fall will.

[JP]

JP: take a look at the The Foundation of The General Theory of Relativity from about page 182 of document 30. ... Einstein talks about conservation of energy and on says on page 185 "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy".

This is exactly what I said in my previous post, actually.  Einstein includes an extra term to account for the gravitational field's energy.  This is where I think anyone trying to figure out work would get into trouble because the interaction between the non-gravitational energy (including masses) and the gravitational energy is going to be highly nontrivial outside of the classical limit.

[Farsight]

Noted, JP. I was backing up what you were saying about the energy of a gravitational field, but also trying to say something about where the brick's potential energy resides. Perhaps this will get it across: imagine you're up in space with two spinning disks in front of you. They're both doing 10000rpm, and both are equipped with revolution counters. Leave one up in space, and take the other one down to the surface of a planet. After a while, compare the counters. Because of the gravitational time dilation, you find that the counter on the disk in space shows a higher reading. So it's spinning at a higher rate, and has more angular momentum / rotational energy than the disk on the surface. The difference is the potential energy. Now think of a brick as a cuboid full of "spinning disks", see http://hyperphysics.phy-astr.gsu.edu/Hbase/nuclear/nspin.html.